Do it has close to the 24 mark as you can.
SW has be known to overbook the flights and whoever check in last gets the boot, and must take the next flight.
It has happen to my family twice now!.

we will be flying delta this time, but this is only b/c Sw pulled out of boston airport
When you were bumped, were you compensated at all? The following is Southwest's official policy - we just did some work with Southwest's mission statement in our Training and Development class, and I read pretty much the whole thing.
http://www.southwest.com/about_swa/customer_service_commitment/csc.pdf Overbooking starts on pg 9)
An oversold flight is a rarity! An oversale takes place when more confirmed Customers
than we expected (and than our aircraft will accommodate) checkin ontime and show up
for the flight leaving one or more confirmed Customers without a seat.
We realize that everyone has a reason to travel. At the same time, we understand that
many travelers are fairly flexible insofar as their departure and arrival times are
concerned. So, when a flight does oversell (again, it is rare), the first thing our Customer
Service Agents do is ask those who have checked in if they are willing to volunteer to
take a later flight. Typically, the incentives we offer result in a number of volunteers
sufficient to free up the seats needed.
Volunteers
If you volunteer to give up your seat in an oversale situation and we can rebook you and
accept your ticket on the next Southwest Airlines flight, we will also give you a travel
voucher in the amount of $100 plus an amount equal to the face value of your remaining
one-way flight coupon(s).
If the flight(s) to your destination immediately after your originally scheduled flight is/are
booked to or beyond capacity, you will be placed on a priority standby list and your
compensation will increase to a travel voucher in the amount of $200 plus an amount
equal to the face value of your remaining one-way flight coupon(s). If you are not
accommodated as a standby Customer, we will confirm you on the next Southwest
Airlines flight(s) with seats available to your destination. You will not incur an increase in
fare.
Involuntary Denied Boarding (Being Bumped)If we do not receive enough volunteers to accommodate all Customers who have
purchased travel and have met our checkin time, any remaining Customer(s) will be
involuntarily denied boarding. We will confirm you on the next Southwest Airlines flight
to your destination with seats available. If your alternative flight(s) is scheduled to arrive
at your destination or stopover point within two hours of your originally scheduled
10
flight(s), we will accept your ticket at no additional charge,
and you will be compensated.We will immediately issue a check or, if you prefer, a travel voucher in an amount equal
to the face value of your remaining one-way flight coupon(s). The maximum amount of
involuntary denied boarding compensation is $400 under these circumstances.
If your alternate flight(s) is scheduled to arrive at your destination or stopover point more
than two hours later than your originally scheduled flight(s), your compensation will
increase to an amount equal to twice your remaining one-way flight coupon(s). In these
cases, the maximum amount of denied boarding compensation increases to $800.
If you are bumped, you will be given a written Notice of Denied Boarding to help you
understand our policies, your compensation, and your travel alternatives.